What are the divisors of 9231?

1, 3, 17, 51, 181, 543, 3077, 9231

There is a total of 8 positive divisors.
The sum of these divisors is 13104.
The arithmetic mean is 1638.

8 odd divisors

1, 3, 17, 51, 181, 543, 3077, 9231

How to compute the divisors of 9231?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 9231 by each of the numbers from 1 to 9231 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

9231 / 1 = 9231 (the remainder is 0, so 1 is a divisor of 9231)
9231 / 2 = 4615.5 (the remainder is 1, so 2 is not a divisor of 9231)
9231 / 3 = 3077 (the remainder is 0, so 3 is a divisor of 9231)
...
9231 / 9230 = 1.0001083423619 (the remainder is 1, so 9230 is not a divisor of 9231)
9231 / 9231 = 1 (the remainder is 0, so 9231 is a divisor of 9231)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 9231 (i.e. 96.0780932367). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

9231 / 1 = 9231 (the remainder is 0, so 1 and 9231 are divisors of 9231)
9231 / 2 = 4615.5 (the remainder is 1, so 2 is not a divisor of 9231)
9231 / 3 = 3077 (the remainder is 0, so 3 and 3077 are divisors of 9231)
...
9231 / 95 = 97.168421052632 (the remainder is 16, so 95 is not a divisor of 9231)
9231 / 96 = 96.15625 (the remainder is 15, so 96 is not a divisor of 9231)